This hinges on the artifact. (So determining what it is will be important!) The suggestion that it was a vase with the likeness of Elwing on it (Elrond's mother, Estel's ancestor) would be reason enough for Elrond to think, this boy needs to learn about his heritage, and the list would be an attempt to place Elwing(?) in the flow of history. So....Elrond is saying something like, 'Elwing was the last heir of Doriath, and mother of Elros, who became the first king of Numenor, whose progeny included Silmarien, the mother of the first Lord of Adunië, whose offspring were the founders of Arnor and Gondor,' so as you can see, she's very important and please show some respect to my stuff.
Not saying we want to do that, but that is the transition - it hinges on the item Estel knocks over while playing/running wild in a place of memory that he is ignorant about.